Integral (sin^2(8x))dx
8x = z
8dx = dz
dx = dz/8
Integral(sin^2(8x))=Integral(sin^2z)dz/8=(1/8)Integral(sin^2z)dz
u = sinz Integralsinzdz = dv
du = cosz -cosz =v
Integral(sin^2z)dz = =( -sinz*cosz +Integral(cos^2z)dz))
cos^2z= 1-sin^2z
Integral(sin^2z)dz = ( -sinz*cosz + Integral(1-sin^2z)dz)
Integral(sin^2z)dz =( -sinz*cosz +Integraldz -Integral(sin^2z)dz)
Integral(sin^2z)dz Integral(sin^2z)dz
--------------------------------------------------------------------------------------------
2*Integral(sin^z)dz =( z -sinzcosz)
Integral(sin^2z)dz = z/2 - sinz*cosz/2
Integral(sin^2z)dz = z/2 - (sin2z)/4
Integral(sin8x)dx = (1/8)(z/2- sin2z/4)= z/16 -( sin2z)/32
Integral(sin8x)dx = 8x/16 - (sin16x)/32 = x/2 - (sin16x)/32 + K